相容次序矩阵AOR迭代收敛的充要条件  

A sufficient and necessary condition of the AOR iterative method for consistently ordered matrices

作　　者：高树玲[1,2] 畅大为[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]周口师范学院数学系,河南周口466001

出　　处：《纺织高校基础科学学报》2009年第2期229-231,共3页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(60671063)

摘　　要：讨论了A为大型稀疏非奇异矩阵的线性方程组Ax=b的AOR迭代求解问题.在系数矩阵A为对角元素非零的(1,1)相容次序矩阵且其相应的Jacob i矩阵的特征值的平方数均为纯虚数或零的情况下,得到了AOR方法收敛的充要条件.并给出一个数值例子对结论作以说明.The AOR iterative method for solving linear systems of the form Ax = b is discussed, where A is a large sparse nonsingular matrix. A sufficient and necessary cndition of the AOR iterative method is given in the case that the cofficient matrix A is （ 1,1 ） consistently ordered matrix and all square of the eigenvalues of its Jaco-bi matrix are pure imaginaries or zeroes. In addition, a numerical example is given for illustrating the results.

关 键 词：相容次序矩阵 AOR迭代法 谱半径 

分 类 号：O241.6[理学—计算数学]